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dc.contributor.author | Beard, Jacob T. B., Jr. | |
dc.contributor.author | Dorris, Ann D. | |
dc.date.accessioned | 2010-05-26T15:54:31Z | |
dc.date.available | 2010-05-26T15:54:31Z | |
dc.date.issued | 1974-09 | |
dc.identifier.uri | http://hdl.handle.net/10106/2178 | |
dc.description.abstract | **Please note that the full text is embargoed** ABSTRACT: Let [see pdf for notation] be a non-negative integral polynomial.
The polynomial P(x) is m-graphical, and a multi-graph G a realization of P(x), provided there exists a multi-graph G containing exactly P(1) points where [see pdf for notation] of these points have degree i for [see pdf for notation]. For multi-graphs G,H having polynomials P(x), Q(x) and number-theoretic partitions (degree sequences) [see pdf for notation], the usual product P(x)Q(x) is shown to be the polynomial of the Cartesian product [see pdf for notation], thus inducing a natural product [see pdf for notation] which extends that of juxtaposing integral multiple copies of [see pdf for notation]. Skeletal results are given on synthesizing a multi-graph G via a natural Cartesian product [see pdf for notation] having the same polynomial (partition) as G. Other results include an elementary sufficient condition for arbitrary non-negative integral polynomials to be graphical. | en |
dc.language.iso | en_US | en |
dc.publisher | University of Texas at Arlington | en |
dc.relation.ispartofseries | Technical Report;15 | |
dc.subject | D-invariant transformation | en |
dc.subject | Polynomials | en |
dc.subject | Multi-graph | en |
dc.subject | Cartesian product | en |
dc.subject.lcsh | Mathematics Research | en |
dc.title | A Polynomial Dual of Partitions | en |
dc.type | Technical Report | en |
dc.publisher.department | Department of Mathematics | en |
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